From b86b6a10373c8c69fe481a43f6a07967205213ec Mon Sep 17 00:00:00 2001
From: Yue Ren <yue.ren.kl@gmail.com>
Date: Wed, 27 Nov 2024 11:00:12 +0000
Subject: [PATCH] TropicalGeometry: tropical_linear_space from graphs

---
 docs/src/TropicalGeometry/linear_space.md |  1 +
 src/TropicalGeometry/linear_space.jl      | 28 +++++++++++++++++++++++
 test/TropicalGeometry/linear_space.jl     |  6 +++++
 3 files changed, 35 insertions(+)

diff --git a/docs/src/TropicalGeometry/linear_space.md b/docs/src/TropicalGeometry/linear_space.md
index e24400084940..0377a47a62bb 100644
--- a/docs/src/TropicalGeometry/linear_space.md
+++ b/docs/src/TropicalGeometry/linear_space.md
@@ -18,6 +18,7 @@ In addition to converting from `TropicalVariety`, objects of type `TropicalLinea
 4. matrices over a field and a tropical semiring map.
     - if matrix over `QQ` and tropical semiring map is trivial, uses an implementation of Rincon's algorithm [Rin13](@cite) in `polymake`
     - for general input, computes minors and uses constructor (2.)
+5. graphs
 ```@docs
 tropical_linear_space
 ```
diff --git a/src/TropicalGeometry/linear_space.jl b/src/TropicalGeometry/linear_space.jl
index df85b285f466..a8e31cc5f784 100644
--- a/src/TropicalGeometry/linear_space.jl
+++ b/src/TropicalGeometry/linear_space.jl
@@ -365,6 +365,34 @@ function tropical_linear_space(I::MPolyIdeal, nu::Union{Nothing,TropicalSemiring
 end
 
 
+@doc raw"""
+    tropical_linear_space(G::Graph, nu::TropicalSemiringMap; weighted_polyhedral_complex_only::Bool=false)
+
+Return the Bergman fan of the graphic matroid of `G` as a tropical linear space, the tropical semiring map `nu` is used to fix the convention.  If `weighted_polyhedral_complex==true`, will not cache any extra information.
+
+# Examples
+```jldoctest
+julia> G = complete_graph(4)
+Undirected graph with 4 nodes and the following edges:
+(2, 1)(3, 1)(3, 2)(4, 1)(4, 2)(4, 3)
+
+julia> tropical_linear_space(G)
+Min tropical linear space
+
+```
+"""
+function tropical_linear_space(G::Graph, nu::Union{Nothing,TropicalSemiringMap}=nothing; weighted_polyhedral_complex_only::Bool=false)
+    M = zero_matrix(QQ,nv(G),ne(G))
+    for (i,edge) in enumerate(edges(G))
+        M[src(edge),i] = 1
+        M[dst(edge),i] = -1
+    end
+    TropG = tropical_linear_space(M,nu;weighted_polyhedral_complex_only=weighted_polyhedral_complex_only)
+    if !weighted_polyhedral_complex_only
+        set_attribute!(TropG,:graph,G)
+    end
+    return TropG
+end
 
 ###############################################################################
 #
diff --git a/test/TropicalGeometry/linear_space.jl b/test/TropicalGeometry/linear_space.jl
index 537cbe8aeddc..b2f7409a0f9a 100644
--- a/test/TropicalGeometry/linear_space.jl
+++ b/test/TropicalGeometry/linear_space.jl
@@ -32,4 +32,10 @@
         @test issetequal(plueckerVector,tropical_pluecker_vector(TropL))
     end
 
+    @testset "tropical linear space from graphs" begin
+        G = complete_graph(3)
+        TropG = tropical_linear_space(G)
+        @test f_vector(TropG) == [0,1,3]
+    end
+
 end